An Invitation Into Joseph`s Mind - Algebra

From time to time I`m asked to tutor KS3 students, and basic algebra is a topic which often comes up. It provides an good example of the methods I use to teach.

A typical problem would be:

2a + 1 = 7

I will first ask the student to demonstrate something for me, even if they say "I don`t know where to start" I ask them to at least try something. Some students will make mistakes such as:

2a = 7 + 1

or

2a = 7 - 1

2a = 6

a = 2x6

But other students, without any workings, say the answer is a = 3 and they question what`s the use in doing such a problem. This is where it`s required to explain why we use algebra at all.

It`s essential that students know the thinking required for such an easy problem as 2a + 1 = 7, because this thinking enables them to answer problems they could not do in their heads, such as:

3.27a - 5.45 = - 4.2

I will then slowly explain the thinking required. Doing reverse operations.

2a + 1 = 7 we can take 1 away from both sides, this cancels the 1

2a + 1 - 1 = 7 - 1

2a = 6 we can divide both sides by 2, this cancels the 2

2a / 2 = 6 / 2 (sometimes its required to present it like this: a x 2 / 2 = 6 / 2 to convey the concept of doing the reverse operation to a)

a = 3

Once we do a few more easy problems that they could also do in their heads such as 10b - 3 = 17, we`re ready to use the concepts of doing reverse operations to answer harder problems.